Verification of Machinery Salvage Value Function

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World J of Engineering and Pure and Applied Sci. 2011;11(3):88
):88
Ekeocha et al
al.,., 2011.
2011 Machinery Salvage Value Function
Short Article
Engineering
ISSN 2249-0582
Verification of Machinery Salvage Value
Function
Rowland Jerry Okechukwu EKEOCHA, Anthony Okay ODUKWE, Jonah Chukwuemeka
AGUNWAMBA
ABSTRACT [ENGLISH/ANGLAIS
[ENGLISH/ANGLAIS]
ANGLAIS]
Affiliations:
Salvage value or resale value is one of the cost components of machinery replacement models. Some replacement models
exclude salvage value in the build-up of cost. Yet it is the value that is adversely affected by deterioration. Various
mathematical formulas for machinery salvage value have been formulated. The formula for salvage value presented by Lake
and Muhlemann is of interest. It is presented in an exponential form. The suitability of this function to our industrial
environment has to be justified bearing in mind that some assets have little or no secondhand value. To ensure a balanced
investigation, efforts are made to obtain salvage values for motor grader, representing large scale industrial environment
and photocopier, representing small and medium scale industrial environment. It is difficult to obtain salvage values because
records are hardly kept for such values. However, two sets of salvage values are obtained for each of the machines. One set is
for the calibration of the salvage value function by Lake and Muhlemann while the other is for comparison between the
measured and predicted salvage values. This paper therefore sets out to investigate and verify the suitability of salvage value
function formulated by Lake and Muhlemann to our industrial environment. It is hoped that the investigation will lead to a
better understanding of the salvage value function for proper application in our industrial environment.
of
Mechanical
Engineering,
University of
Nigeria, Nsukka,
NIGERIA
2 Faculty
of
Engineering,
University of
Nigeria, Nsukka,
NIGERIA
Address for
Correspondence/
Adresse pour
la Correspondanc
e:
ekeochaj@yahoo.
com
Keywords: Salvage value, replacement models, verification
RÉSUMÉ [FRANÇAIS/FRENCH]
FRANÇAIS/FRENCH]
La valeur de récupération ou de la valeur de revente est l'une des composantes du coûtdes modèles de remplacement des
machines. Certains
modèles de
remplacementd'exclure la
valeur
de
récupération dans
l'accumulation
de coûts. Pourtant, c'est la valeurqui est affectée par la détérioration. Diverses formules mathématiques pour la valeur de
récupération des machines ont été formulées. La formule pour la valeur de récupérationprésentés par Lake
et Muhlemann est d'un intérêt. Il est présenté dans une forme exponentielle. La pertinence de cette fonction pour notre
environnement industriel doit êtrejustifié portant à l'esprit que certains actifs ont peu ou pas de valeur d'occasion. Afin de
garantir une enquête équilibrée, des efforts sont déployés pour obtenir des valeurs de récupération pour les niveleuses,
représentant l'environnement industriel à grande échelleet d'un photocopieur, représentant les petites et
moyennes environnement à l'échelle industrielle. Il est difficile d'obtenir des valeurs de récupération parce que les
dossiers ne sont guère conservés pour de telles valeurs. Cependant, deux ensembles de valeurs de récupération sont obtenus
pour chacune des machines. Un ensemble est pour le calibrage de la fonction de valeur de récupération par le lac et
les Muhlemann tandis que l'autre est pour la comparaison entre les valeurs de récupération mesurés et prédits. Ce
document vise donc à enquêter et de vérifier l'adéquation de la fonction valeur de récupération formulée par Lake
et Muhlemann à notre environnement industriel. Il est à espérer que l'enquête va conduire à une meilleure
compréhension de la fonction de valeur de récupération pour une application correcte de notre environnement industriel.
Mots-clés: La valeur de récupération, des modèles de remplacement, la vérification.
INTRODUCTION
1 Department
Accepted/Accepté
: November, 2011
Citation: Ekeocha
RJO, Odukwe
AO, Agunwamba
JC. Verification of
Machinery
Salvage Value
Function. World
Journal of
Engineering and
Pure and Applied
Sciences
2011;1(2):88-90.
service or economic life especially where an active resale
Salvage value refers to the proceeds from the sale of
market does not exist. Records are not usually kept for
second hand plant/machine.
It depends on the
the scrap values and no value is usually placed on the
conditions of the plant/machine at the point of sale. Such
cannibalized parts of such machinery. A way of
conditions include deterioration, the service life (man-
predicting salvage value for machinery replacement
hour), maintenance history and the capacity of the
models has to be sought. Various mathematical formulas
plant/machine. Records for salvage values of machinery
for machinery salvage value have been presented [1-3].
are not easy to achieve when compared to records for the
Lake and Muhlemann [4] formulated a salvage value
cost prices of similar machinery. Most machinery and
function that is in exponential form. There is therefore
equipment are scrapped or cannibalized after their
the need to verify the suitability of the function to our
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© Research | Reviews | Publications, 2011
http://www.rrpjournals.com/
ISSN 2249-0582
World J of Engineering and Pure and Applied Sci. 2011;11(3):89
):89
Ekeocha et al.,
al., 2011.
2011 Machinery Salvage Value Function
OPEN
ACCESS
industrial environment since it is one of the cost
value of the correlation coefficient between the measured
components in most machinery replacement models.
and the predicted salvage values gives an indication of
The objective of this paper is to verify the suitability of
the suitability of the salvage value function to our
salvage value function by Lake and Muhlemann [4] to
industrial environment.
our industrial environment.
IMPLEMENTATION
METHODOLOGY
The salvage value function by Lake and Muhlemann [4]
The methodology is a combination of analytical and
is given by
experimental processes. The processes begin with the
collection of two sets each of measured (actual) salvage
Where
S(t) = Salvage Value
values for CAT 140H Motor Grader and SHARP SF-2035
Q = Cost of Machine
Photocopier (Field Data) followed by the calibration of
d = Deterioration
the salvage value function using a set of the field data to
t = Time (age)
obtain values for deterioration. The next step is to use the
calibrated salvage value function to predict salvage
CALIBRATION OF THE FUNCTION
values for the Motor Grader and Photocopier. Another
The regression line [5] is given by
set of field data is then used to plot separate graphs of
measured and predicted salvage values of the machines
for comparison. Finally the correlation coefficients
And the slope of the regression line is given by
between the measured and predicted salvage values of
the Grader and Photocopier are derived to ascertain the
strength and linear dependence of the two variables. The
Table 1:
This Table shows variation of salvage value with Age of Motor Grader and Photocopier
t
2
3
4
5
6
7
8
9
10
11
12
13
S(t)g
248500
230000
210000
194000
163500
161000
155250
161000
137500
104500
105000
98500
S(t)p
145000
135000
120000
115000
100000
95000
90000
85000
84000
S(t)g = Salvage Value of the Grader in Dollars; S(t)p = Salvage Value of the Photocopier in Naira; t = Age in Years
Source: Resale market (Grader), Business centre (Photocopier)[6]
Table 2:
This Table shows variation of Measured and Predicted Salvage Values S(t) with Age of Motor Grader and
Photocopier
Age
t
Measured Salvage
Value of the Motor
Grader
Predicted Salvage
Value of the Motor
Grader
1
Measured Salvage Value
of the Photocopier
Predicted Salvage Value
of the Photocopier
140000
142935
2
264500
258683
130000
136203
3
227750
237396
120000
129788
4
214000
218854
110000
123675
5
184750
201302
100000
117850
6
158750
185157
90000
112299
7
152000
170307
80000
107010
8
147250
156649
75000
101969
9
161000
144086
60000
97167
10
109500
132530
11
104500
121901
12
105000
112125
13
94250
103132
© Research | Reviews | Publications, 2011
http://www.rrpjournals.com/
OPEN
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ISSN 2249-0582
World J of Engineering and Pure and Applied Sci. 2011;11(3):90
):90
Ekeocha et al.,
al., 2011.
2011 Machinery Salvage Value Function
OPEN
ACCESS
Applying the least square method on the data in Table 1,
suitable for application in the small and medium scale
b = - 0.0363 and d = 0.0802 for the Grader
industrial environment. It is of interest to note that both
b = -0.02096 and d = 0.0471 for the Photocopier
the
Grader
and
Photocopier
have
remarkable
secondhand value (Tables 1 and 2). The percentage
Q = $305760 for the Grader and N150000 for the
deviation between the measured and predicted salvage
Photocopier
values is generally low with absolute values ranging
from 2.22 to 17.38% for the Grader and 2.05 to 38.25% for
Figure 1:
This figure shows comparison of the measured
the Photocopier.
and predicted salvage values of grader
CONCLUSION
The measured and predicted salvage values are
positively correlated with correlation coefficient of 0.98
for the Grader and unity for the Photocopier.
The
salvage value function by Lake and Muhlemann [4] is
therefore suitable to our industrial environment. The
remarkable secondhand value of both machines is
worthy of note. The generally low absolute values of the
percentage
deviation
between
the
measured
and
predicted salvage values of both the Grader and
Photocopier is another indication of the suitability of the
salvage value function to our industrial environment.
REFERENCES
Figure 1:
This figure shows comparison of the measured
[1] Arora SR, Lele PT. A note on optimal maintenance
policy and sale date of a machine, Management
and predicted salvage values of photocopier
Science, 1970, vol.17, no.3, p.170-3.
[2] Glassier
GJ.
The
age
replacement
Technometrics, 1967, vol.9,
problem,
p.89-91.
[3] Kamien NL, Schwartz MI. Optimal maintenance and
sale
age
for
a
machine
subject
to
failure,
Management Science, 1971, vol.17B, p.495-504.
[4] Lake
DH,
Muhlemann
AP.
An
equipment
replacement problem, Journal of operational society,
1979, vol.30, p.405-11.
[5] Ekeocha RJO. Dynamic modeling of machinery
replacement problems, a thesis for the award of
DISCUSSION
doctorate degree in the department of mechanical
The measured and predicted salvage values of the Motor
engineering, University of Nigeria, Nsukka, 2011.
Grader are linearly dependent with a correlation
[6] Machinery resale market, Abuja for the Grader and
coefficient of 0.98 (figure 1). This is an indication of the
Business centres Abuja, Nigeria for the photocopier,
suitability of the salvage value function by Lake and
2011.
Muhlemann [4] to the large scale industrial environment.
The measured and predicted salvage values of the
ACKNOWLEDGEMENT / SOURCE OF SUPPORT
Photocopier
Nil
also show
a
high
degree
of
linear
dependence of the two variables with a correlation
coefficient of unity (figure 2). This means that the salvage
CONFLICT OF INTEREST
value function by Lake and Muhlemann [4] is very
No conflict of interests was declared by authors.
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